Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(C_4\times C_{12}\)
Signature \([ 0; 4, 12, 12 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $C_4\times C_{12}$
Group identifier: [48,20]
Signature: $[ 0; 4, 12, 12 ]$
Conjugacy classes for this refined passport: 7, 33, 44

The full automorphism group for this family is $D_{12}:C_4$ with signature $[ 0; 2, 8, 12 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E\times A_{2}\times A_{2}\times A_{2}\times A_{2}\times E\times A_{2}\times E$
Corresponding character(s): 7, 8, 10, 21, 22, 23, 24, 25, 26, 27

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.48-20.0.4-12-12.1.1

  (1,13,2,14) (3,15,4,16) (5,17,6,18) (7,19,8,20) (9,21,10,22) (11,23,12,24) (25,37,26,38) (27,39,28,40) (29,41,30,42) (31,43,32,44) (33,45,34,46) (35,47,36,48)
  (1,29,11,27,5,33,3,31,9,25,7,35) (2,30,12,28,6,34,4,32,10,26,8,36) (13,41,23,39,17,45,15,43,21,37,19,47) (14,42,24,40,18,46,16,44,22,38,20,48)
  (1,48,8,37,9,44,4,45,5,40,12,41) (2,47,7,38,10,43,3,46,6,39,11,42) (13,35,20,26,21,31,16,34,17,27,24,30) (14,36,19,25,22,32,15,33,18,28,23,29)